Question: Solve for $x$ and $y$ using elimination. $\begin{align*}4x+y &= -1 \\ -4x-8y &= 8\end{align*}$
We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-7y = 7$ Divide both sides by $-7$ and reduce as necessary. $y = -1$ Substitute $-1$ for $y$ in the top equation. $4x- 1 = -1$ $4x-1 = -1$ $4x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = -1$.